How fast is a GPU compared to a CPU for training deep learning models, and which GPU should I buy?
I think you should redirect your focus.
Learn and play with ML, and only when compute becomes the main bottleneck for your learning, invest in hardware.

I've recently engaged into a ML project for which I 've assembled a machine with gtx1080, installed gui-less ubuntu, configured ssh, drivers etc, and than spend 3 months on data collection. And the dataset was so small (30k images), that I could probably learn mobilenet v3 on my CPU instead.

I think that in most cases focusing on hardware is a form of procrastination when it comes to machine learning.
Also, a laptop with really strong GPU makes little sense (unless it's really well cooled like Alienware r3 that I use at work, but it's to heavy to be really considered a laptop...). It will throttle, It will be less durable due to constant overheating when you learn models.

So I'd say, go for gtx1060 laptop and only when you really need compute (you think you have a chance to actually win a competition due to a great idea you have, or you have a client that has seen a demo and really want's to pay for your model if you improve it), invest into standalone PC or cloud to tune your prototype model.